Multivariable And Parametric Functions

## Description

Suppose we wanted to turn the multivariable function,

(1)
$$f(x, y) = (x^4 - 5x^2 + 4 + y^2)^2$$

into a parametric function, where

(2)
$$x = f(t) = 2t + 5$$

and

(3)
$$y = g(t) = 3t - 1$$

We can use Sage to accomplish this.

## Sage Cell

#### Code

var('y t')
f(x, y) = (x^4 - 5*x^2 + 4 + y^2)^2
f(x=2*t+5, y=3*t-1)


## Options

#### Expanding the output

The above cell produces a correct, but not easily readable output. We can clean it up with .expand()

#### Code

var('y t')
f(x, y) = (x^4 - 5*x^2 + 4 + y^2)^2
f(x=2*t+5, y=3*t-1).expand()


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